学 术 报 告

报告题目: Numerical Computation for Nonnegative Matrix Factorization

报告人：储德林，新加坡国立大学教授，博士生导师

报告时间：2025年6月26日(周四)9:30-12:00

报告地点：崇礼楼(理学院)403

储德林，新加坡国立大学教授，博士生导师。1991年获清华大学博士学位，主要从事数值线性代数、科学计算、数值分析、矩阵理论及计算等方面的研究。现为多个国际顶尖SCI杂志AE,包括自动化顶尖期刊

Automatica, SIAM Journal on Scientific Computing, SIAM Journal on Matrix Analysis and Applications。

摘要：Nonnegative matrix factorization (NMF) is a prominent technique for data dimensionality reduction. In this talk, a framework called ARKNLS (Alternating Rank-k Nonnegativity constrained Least Squares) is introduced for computing NMF. First, a recursive formula for the solution of the rank-k nonnegativity-constrained least squares (NLS) is established.This recursive formula can be used to derive the closed-form solution for the Rank-k NLS problem for any integer k. As a result, each subproblem for an alternating rank-k nonnegative least squares framework can be obtained based on this closed forin solution. This talk is then focused on the framework with=3)，which leads to a new algorithm for NMF via the closed-form solution of the rank-3 NLS problem. Furthermore, a new strategy that efficiently overcomes the potential singularity problem in rank-3 NLS within the context of NMF computation is also presented. Extensive numerical comparisons using real and synthetic data sets demonstrate that the proposed algorithm provides state-of-the-art performance in terms of computational accuracy and çpu time.